Fixed point problems for generalized contractions with applicationsopen access
- Authors
- Nazam, Muhammad; Park, Choonkil; Arshad, Muhammad
- Issue Date
- May-2021
- Publisher
- SPRINGER
- Keywords
- Fixed point; (psi,theta)-contraction; Complete metric space; Applications
- Citation
- ADVANCES IN DIFFERENCE EQUATIONS, v.2021, no.1, pp.1 - 15
- Indexed
- SCIE
SCOPUS
- Journal Title
- ADVANCES IN DIFFERENCE EQUATIONS
- Volume
- 2021
- Number
- 1
- Start Page
- 1
- End Page
- 15
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/141972
- DOI
- 10.1186/s13662-021-03405-w
- ISSN
- 1687-1839
- Abstract
- In this paper, we investigate the conditions on the control mappings psi,phi : (0, infinity) -> R that guarantee the existence of the fixed points of the mapping T : X -> P(X) satisfying the following inequalities: psi (H (Tx, Ty)) <= phi (d(x, y)) for all x,y epsilon X, provided that H (Tx, Ty) > 0, and psi(H(Tx, Ty)) <= phi (A(x, y)) for all x, y epsilon X, provided that H(Tx, Ty) > 0, where A (x, y) = max{d(x,y), d (x, Tx), d (y, Ty), (d (x, Ty) + d (Tx, y))/2}, and (X, d) is a metric space. The obtained fixed point results improve many earlier results on the set-valued contractions. As an application, we consider the existence of the solutions of an FDE.
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